X ray diffraction

Essential Parts of the Diffractometer

• X-ray Tube: the source of X Rays• Incident-beam optics: condition the X-ray beam

before it hits the sample• The goniometer: the platform that holds and

moves the sample, optics, detector, and/or tube• The sample & sample holder• Receiving-side optics: condition the X-ray beam

after it has encountered the sample• Detector: count the number of X Rays scattered

by the sample

• Production of X-Rays• Collimator• Monochromator

Filter Crystal monochromator

• Detector Photographic methods Counter methods

Instrumentation

The wavelength of X rays is determined by the anode of the X-ray source.

• Electrons from the filament strike the target anode, producing characteristic radiation via the photoelectric effect.

• The anode material determines the wavelengths of characteristic radiation.• While we would prefer a monochromatic source, the X-ray beam actually consists

of several characteristic wavelengths of X rays.

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Bragg’s law is a simplistic model to understand what conditions are required for diffraction.

• For parallel planes of atoms, with a space dhkl between the planes, constructive interference only occurs when Bragg’s law is satisfied. – In our diffractometers, the X-ray wavelength is fixed.– Consequently, a family of planes produces a diffraction peak only at a specific angle .– Additionally, the plane normal must be parallel to the diffraction vector

• Plane normal: the direction perpendicular to a plane of atoms• Diffraction vector: the vector that bisects the angle between the incident and diffracted beam

• The space between diffracting planes of atoms determines peak positions. • The peak intensity is determined by what atoms are in the diffracting plane.

sin2 hkld dhkl

dhkl

XRD-Methods

• Laue photographic method• Braggs X-Ray spectrometer• Rotating crystal method• Powder method

Laue photographic method• In his first experiments, Max von Laue (Nobel Prize in Physics in 1914)

used continuous radiation (with all possible wavelengths) to impact on a stationary crystal. With this procedure the crystal generates a set of diffracted beams that show the internal symmetry of the crystal. In these circumstances, and taking into account Bragg's Law, the experimental constants are the interplanar spacings d and the crystal position referred to the incident beam. The variables are the wavelength λ and the integer number n:

n λ = 2 dhkl sin θnh,nk,nl

• Thus, the diffraction pattern will contain (for the same spacing d) the diffracted beams corresponding to the first order of diffraction (n=1) of a certain wavelength, the second order (n=2) of half the wavelength (λ/2), the third order (n=3) with wavelength λ/3, etc. Therefore, the Laue diagram is simply a stereographic projection of the crystal

The Laue method in transmission mode The Laue method in reflection mode

Laue diagram of a crystal

Braggs X-Ray spectrometer

When x-rays are scattered from a crystal lattice, peaks of scattered intensity are observed which correspond to the following conditions:

1.The angle of incidence = angle of scattering.

2.The pathlength difference is equal to an integer number of wavelengths.The condition for maximum intensity contained in Bragg's law above allow us to calculate details about the crystal structure, or if the crystal structure is known, to determine the wavelength of the x-rays incident upon the crystal.

X-radiation for diffraction measurements is produced by a sealed tube or rotating anode.

• Sealed X-ray tubes tend to operate at 1.8 to 3 kW.

• Rotating anode X-ray tubes produce much more flux because they operate at 9 to 18 kW. – A rotating anode spins the anode at 6000

rpm, helping to distribute heat over a larger area and therefore allowing the tube to be run at higher power without melting the target.

• Both sources generate X rays by striking the anode target wth an electron beam from a tungsten filament.– The target must be water cooled.– The target and filament must be

contained in a vacuum.

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Rotating crystal method

Most of our powder diffractometers use the Bragg-Brentano parafocusing geometry.

• A point detector and sample are moved so that the detector is always at 2 and the sample surface is always at to the incident X-ray beam.

• In the parafocusing arrangement, the incident- and diffracted-beam slits move on a circle that is centered on the sample. Divergent X rays from the source hit the sample at different points on its surface. During the diffraction process the X rays are refocused at the detector slit.

• This arrangement provides the best combination of intensity, peak shape, and angular resolution for the widest number of samples.

F: the X-ray sourceDS: the incident-beam divergence-limiting slitSS: the Soller slit assemblyS: the sampleRS: the diffracted-beam receiving slitC: the monochromator crystalAS: the anti-scatter slit

What is X-ray Powder Diffraction (XRD)

X-ray powder diffraction (XRD) is a rapid analytical technique primarily used for phase identification of a crystalline material and can provide information on unit cell dimensions.

The analyzed material is finely ground, homogenized, and average bulk composition is determined.

Fundamental Principles of X-ray Powder Diffraction (XRD)

Max von Laue, in 1912, discovered that crystalline substances act as three-dimensional diffraction gratings for X-ray wavelengths similar to the spacing of planes in a crystal lattice.

X-ray diffraction is now a common technique for the study of crystal structures and atomic spacing.

X-ray diffraction is based on constructive interference of monochromatic X-rays and a crystalline sample.

These X-rays are generated by a cathode ray tube, filtered to produce monochromatic radiation, collimated to concentrate, and directed toward the sample. The interaction of the incident rays with the sample produces constructive interference (and a diffracted ray) when conditions satisfy Bragg's Law (nλ=2d sin θ).

This law relates the wavelength of electromagnetic radiation to the diffraction angle and the lattice spacing in a crystalline sample.

These diffracted X-rays are then detected, processed and counted.

By scanning the sample through a range of 2θangles, all possible diffraction directions of the lattice should be attained due to the random orientation of the powdered material.

Conversion of the diffraction peaks to d-spacings allows identification of the mineral because each mineral has a set of unique d-spacings. Typically, this is achieved by comparison of d-spacings with standard reference patterns.

All diffraction methods are based on generation of X-rays in an X-ray tube. These X-rays are directed at the sample, and the diffracted rays are collected.

A key component of all diffraction is the angle between the incident and diffracted rays. Powder and single crystal diffraction vary in instrumentation beyond this.

Applications of XRD

• XRD is a nondestructive technique • To identify crystalline phases and orientation• To determine structural properties:• Lattice parameters (10-4Å), strain, grain size, expitaxy,

phase composition, preferred orientation (Laue) order-disorder transformation, thermal expansion

• To measure thickness of thin films and multi-layers

• To determine atomic arrangement• Detection limits: ~3% in a two phase mixture; can be ~0.1% with synchrotron radiationSpatial resolution: normally none

Applications •X-ray powder diffraction is most widely used for the identification of unknown crystalline materials (e.g. minerals, inorganic compounds). Determination of unknown solids is critical to studies in geology, environmental science, material science, engineering and biology. Other applications include

• characterization of crystalline materials

• identification of fine-grained minerals such as clays and mixed layer clays that are difficult to determine optically

• determination of unit cell dimensions measurement of sample purity

With specialized techniques, XRD can be used to:

• determine crystal structures using Rietveld refinement

• determine of modal amounts of minerals (quantitative analysis)

• make textural measurements, such as the orientation of grains, in a polycrystalline sample

• characterize thin films samples by:

determining lattice mismatch between film and substrate and to inferring stress and strain determining dislocation density and quality of the film by rocking curve measurements measuring superlattices in multilayered epitaxial structures determining the thickness, roughness and density of the film using glancing incidence X-ray reflectivity measurements

Strengths and Limitations of X-ray Powder Diffraction (XRD)?

Strengths

Powerful and rapid (< 20 min) technique for identification of an unknown mineral

In most cases, it provides an unambiguous mineral determination Minimal sample preparation is required

XRD units are widely available

Data interpretation is relatively straight forward

Limitations Homogeneous and single phase material is best for identification of an unknown

Must have access to a standard reference file of inorganic compounds (d-spacings, hkls)

Requires tenths of a gram of material which must be ground into a powder

For mixed materials, detection limit is ~ 2% of sample For unit cell determinations, indexing of patterns for non-isometric crystal systems is complicated

Peak overlay may occur and worsens for high angle 'reflections'

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